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Research Papers

Self-Similarity in Vibration Time Series: Application to Gear Fault Diagnostics

[+] Author and Article Information
S. J. Loutridis

Sensors and Instrumentation Laboratory, Department of Electrical Engineering, School of Technological Applications, Technological Educational Institute of Larissa, GR 41-110 Larissa, Greeceloutridi@teilar.gr

J. Vib. Acoust 130(3), 031004 (Apr 03, 2008) (9 pages) doi:10.1115/1.2827449 History: Received January 08, 2007; Revised November 07, 2007; Published April 03, 2008

The vibration time series of gear systems exhibit self-similarity. The time-series behavior is characterized by an exponent, known as the scaling exponent. An algorithm is proposed for the estimation of both global and local exponents, thus providing a means of examining the time-series fine structure. The proposed algorithm is applied to experimental data recorded from gear pairs with localized defects in the form of bending fatigue cracks. It is shown that an examination of the exponent empirical histogram allows detection of damage at an early stage and also provides an estimate of the defect magnitude.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Detrending using the LSA, scale=20

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Figure 3

Detrending using the DFA, window of 20 points

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Figure 4

Experimental setup

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Figure 5

PSD for the case of a gear pair with tooth loss (top), 33% crack (middle), and healthy gear pair (bottom)

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Figure 12

Empirical histogram (bars) and singularity spectrum (dashed line) of a gear pair with 33% crack

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Figure 13

Empirical histogram for the case of a healthy gear pair (left) and a gear pair suffering tooth loss (right)

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Figure 14

Mean exponent and skewness of pdf as a function of crack magnitude

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Figure 15

Three-dimensional plot of wavelet coefficients over the time-scale plane

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Figure 16

Prediction of crack advancement based on the wavelet coefficients

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Figure 1

Weighting function φ at scales s=10, s=20, and s=40

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Figure 6

Slope derived from the power spectrum: a healthy gear pair (upper) and a pair with 33% crack (lower). The rotational speed was 300rpm and the load was 10Nm.

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Figure 7

Fluctuation versus scale for a healthy gear pair (left) and a pair with 33% crack (right)

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Figure 8

Vibration time series and fluctuation for a gear pair with 33% crack (300rpm, 18Nm)

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Figure 9

Scaling exponent as a function of time for a gear pair with 33% crack (300rpm, 18Nm)

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Figure 10

Scaling exponent as a function of time for a healthy gear pair (300rpm, 18Nm)

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Figure 11

Scaling exponent h(q) as a function of moment q

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